The Bush administration faces growing challenges in holding together the 32-nation coalition deployed in Iraq, with four countries already gone, another four due to leave by September and others now making known their intention to wind down or depart before the political transition is complete next year, according to officials from 28 participating countries.

The drama over the Filipino hostage in Iraq, which led the Philippines government to say this week that it will pull out before its August mandate expires, is only the latest problem -- and one of the smaller issues -- in U.S. efforts to sustain the 22,000-strong force that, with 140,000 U.S. troops, forms the multinational force trying to stabilize postwar Iraq.

Norway quietly pulled out its 155 military engineers this month, leaving behind only about 15 personnel to assist a new NATO-coordinated effort to help train and equip Iraqi security forces. New Zealand intends to pull out its 60 engineers by September, while Thailand plans to withdraw its more than 450 troops that same month, barring a last-minute political reversal that Thai officials consider unlikely, say envoys from both countries. "It's 90 percent definite that we're going," a Thai diplomat said.

The Netherlands is likely to pull out next spring after the first of three Iraqi elections, while Polish military officials told the Pentagon that Poland's large contingent will probably leave in mid-2005, other diplomats say.

Any dwindling of the coalition -- by choice or after hostage seizures and other violence -- further complicates the already difficult job of sustaining the multinational force, which is critical to Washington's assertion that it has international support for the Iraq mission. It could also encourage further abductions or attacks to heighten the psychological pressure and undermine the U.S.-led mission, coalition diplomats say.

"We think withdrawal sends the wrong signal and that it is important for people to stand up to terrorists and not allow them to change our behavior," State Department spokesman Richard Boucher told reporters.

Some attrition was inevitable after the U.S.-led occupation officially ended on June 28, say envoys in Washington. "This was expected as sovereignty was handed over. Some have been desperate to get out of there, because they were handcuffed to the process," said a diplomat from a prominent member of the coalition who spoke on the condition of anonymity because of the sensitivity of the issue.

"In certain countries, public opinion was against them going in -- so they were under political pressure that they either shouldn't be there or they should be there only for so long. Sovereignty was always a point at which countries look at how long they'll stay. It becomes a segue for pulling out," he added.

To track commitments, the Bush administration keeps a color-coded chart of coalition members: red for countries withdrawing, yellow for nations considering a pullout and green for countries staying.

The size and abilities of the coalition forces have been a source of controversy and embarrassment for the administration since the war to oust Iraqi leader Saddam Hussein.

In many ways, the symbolic importance of international participation has been at least as vital for the Bush administration as the often-limited military role the troops have played. And while administration officials have stressed the number of countries that have sent troops, others have noted the small size of many military contingents and the continued absence of some major powers.

Several participating countries sent fewer than 100 troops. In other cases, forces diminished significantly over time. Moldova's contingent is the smallest -- down to 12 from 42. Singapore has quietly reduced its presence from 191 to 33.

The Bush administration contends the coalition is holding, pointing to the renewed troop commitments from large contributors such as Britain and Italy. "Their support has solidified as the political process has come to pass," said Lincoln Bloomfield, assistant secretary of state for political-military affairs.

"If you look at how many voices were doubting that the transfer of sovereignty would actually occur, you can now see a momentum behind the military coalition to rally around the Iraqi government and complete the process all the way through the electoral stages leading to full sovereignty at the end of 2005. Despite all the security challenges, the big picture is that the plan is working," Bloomfield said.

El Salvador renewed its commitment of 380 troops after President Bush hosted Salvadoran President Antonio Saca at the White House this week, the latest of several White House visits by leaders of coalition countries. Lithuania renewed its 105-troop commitment last week.

Several other countries have promised to significantly add to their contingents. South Korea is increasing its force from 600 to 3,700, while Azerbaijan offered an additional 250 soldiers to join the 150 already in Iraq. Georgia said it is ready to more than double its 159 troops -- to more than 400.

"We don't see any major defections; we see troops coming and going as they said they would; and there have been more plus-ups than withdrawals," said a senior Pentagon official involved in Iraq policy.

But some pledges the administration cites are misleading or contain caveats that call into question whether many troops will stay much beyond the first round of Iraqi elections scheduled for January.

Australia's pledge to increase its commitment will bring its troop strength to 880 -- fewer than half the 2,000 troops it had during the war. And only about 250 are in Iraq, with the rest in air and naval support positions nearby, Australian envoys say. For Australia and some other countries, increases are mainly meant to enhance security for their own troops, embassies and personnel.

Support is also tenuous in nations Washington considers to be key players. The vote this week in Italy's House of Deputies to extend its deployment was 257 to 207, a reflection of the almost even public split, an Italian envoy said. Playing to strong public antiwar sentiment, Australia's opposition pledged to withdraw troops by Christmas if elected, while revelations about the Abu Ghraib prison abuse led Hungary's opposition to call for a withdrawal despite originally supporting the deployment.

Hostage seizures of nationals from Japan, South Korea, Poland, Italy, Bulgaria, the Philippines and the United States have heightened public and political pressure, with several countries expecting debates to intensify this fall.

The first blow to the U.S.-led force was the decision by new Spanish Prime Minister Jose Luis Rodriguez Zapatero to withdraw his country's 1,300 troops, which led Honduras and the Dominican Republic to bring home their few hundred troops this spring. Britain and Spain had been the two closest U.S. allies in the Iraq war. Zapatero's election upset after a terrorist bombing at a Madrid train station deepened opposition to Spain's deployment.

For other countries, however, the issue is capability. "We have limited resources and huge commitments, like Afghanistan, the Solomon Islands, Bosnia, Kosovo and Timor," a New Zealand diplomat said. "Hostage dramas have not influenced our plans or thinking, and it was not a political decision. We're just stretched."

The countries most committed to staying are East European and former Soviet countries. "We benefited in our own recent history from foreign peacekeepers, so we understand the value of action. Our stand on Iraq is firm, and our participation is not questionable," said Macedonian Ambassador Nikola Dimitrov.

The day Spain pulled out, Albania wrote Washington to reaffirm its commitment and has since pledged to increase its troops from 71 to 200. "We're the most pro-U.S. nation in Europe," Ambassador Satos Tarisa said, "and we're in Iraq for the long haul."